With devices of the kind referred above, large-area sheet webs, as frequently used for insulation or for the sealing of roofs, floors or walls in buildings, can be welded together. In the weld area preceding the press-on roller, a "pocket" is formed by the heating nozzle between the overlapping sheet edges, hot air being blown into it to melt the sheet surface; this pocket is to be limited laterally by applied hold-down means and is to be closed. In known machines of this kind, difficulties arise, especially in the case of relatively thick sheets, because the press-on roll does not apply tightly for its entire width as a result of an oblique position of the machine frame. Furthermore, since driven as well as idle rollers are provided at the machine frame, upsetting and rippling often occurs during travel of the machine. In addition, the snug bearing contact of the machine and, in particular, the closure of the "pocket" is often interfered with by the hold-down means when traveling over uneven surfaces. Hence, reliable welding is not assured, and there is particular danger that if the "pocket" is not tightly closed on the side, hot air will be blown under one sheet web, which may thereby be lifted up.